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arXiv · 1411.4795

Weak-local derivations and homomorphisms on C*-algebras

Ahlem Ben Ali Essaleh·Antonio M. Peralta·María Isabel Ramírez
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Abstract

We prove that every weak-local derivation on a C$^*$-algebra is continuous, and the same conclusion remains valid for weak$^*$-local derivations on von Neumann algebras. We further show that weak-local derivations on C$^*$-algebras and weak$^*$-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal $^*$-automorphism with our notions of extreme-strong-local derivations and automorphisms.

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BibTeXRIS

Ahlem Ben Ali Essaleh, Antonio M. Peralta, María Isabel Ramírez. 2014-11-18. Weak-local derivations and homomorphisms on C*-algebras. https://arxiv.org/abs/1411.4795

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